A Rolling Beta tracks how an asset's systematic risk—its sensitivity to the market—evolves through time. Instead of estimating a single, "static" CAPM β from the full sample, we:
Slice the return history into overlapping (or calendar) windows.
Estimate β separately inside each window (usually via an OLS regression of excess returns on market excess returns).
Stitch those estimates together to create a time-series of β values.
The result is a curve that answers:
"Was this stock defensive in 2020 but high-beta in 2021?"
| Insight | Practical Action |
|---|---|
| Regime shifts – β drifts upward in bull runs, collapses in crises. | Adjust hedging or leverage dynamically. |
| Style changes – a fund once market-neutral may become directional. | Performance attribution & manager monitoring. |
| Stress testing – identify periods when β spiked > 1.5 (higher draw-down risk). | Scenario analysis & risk-budget alerts. |
Rolling β is therefore a key input for tactical asset allocation, risk budgeting, and manager due-diligence.
Window length: 1 calendar year (≈ 252 trading days).
Rationale: strikes a balance between statistical power and responsiveness.
Frequency: Daily returns.
# srv.py → compute_yearly_betas()
df = pd.DataFrame({"p": port_excess, "b": bench_excess})
beta_y = df.groupby(df.index.year).apply(
lambda g: g["p"].cov(g["b"]) / g["b"].var()
)Converts daily excess returns to a common calendar year.
Uses the covariance / variance formula (mathematically identical to the OLS slope).
Returns a {year: β} dictionary, which your frontend plots as the Rolling Betas line chart.
(Your results page overlays the "market β = 1" line for quick context.)
For a given window $t=1,\dots,T$:
Tip: overlapping windows (e.g., 252-day rolling with daily step) give smoother curves but require more computation. You chose calendar-year buckets—excellent for quick visual stories.
| Pattern | Meaning | Possible Action |
|---|---|---|
| Steady β ≈ 1 | Market-like behaviour | Hold as core allocation |
| β trending ↑ | Becoming more cyclical / growth-tilted | Reduce weight or hedge |
| β < 0 episode | Acts as market hedge (rare) | Exploit for diversification |
| Erratic β | Unstable factor exposures | Review strategy, increase monitoring |
Always cross-check with p-values / R² if sample size is small.
| Issue | Recommendation |
|---|---|
| Window length trade-off | Short → noisy; Long → lags. Test 6-m vs 1-y vs 3-y. |
| Benchmark choice | Use the same index your investors benchmark against (NIFTY 50, S&P 500…). |
| Non-stationarity | Combine rolling β with time-series break tests to alert when behaviour changes statistically. |
| Leverage / derivatives | Un‐dampened β can explode if the portfolio carries leverage. Scale exposure before regression. |
Rolling and – parallel time-series reveal skill drift and explanatory power.
Downside Beta – compute β using only market down-days for crash sensitivity.
Multi-factor rolling – size, value, momentum betas over time (uses Fama-French regressions).
Dynamic risk measurement: Captures time-varying market sensitivity that static beta measures miss completely.
Regime identification: Helps identify market regime changes and how investments respond differently across cycles.
Style drift detection: Reveals when investment managers deviate from their stated strategy or factor exposures change.
Intuitive visualization: Provides an accessible way to visualize risk evolution through time for non-technical stakeholders.
Forward-looking insights: Historical beta patterns during similar market conditions can inform future expectations.
Statistical noise: Shorter estimation windows increase responsiveness but reduce statistical reliability of beta estimates.
Lagging indicator: By definition, rolling beta looks backward and may not accurately predict future market sensitivity.
Window selection bias: Results depend heavily on the chosen window length and can differ significantly between implementations.
Single-factor limitation: Standard rolling beta only captures market risk, ignoring other systematic risk factors.
Benchmark dependency: Results are only meaningful relative to the specific benchmark used in the calculation.
Rolling Betas turn a single risk number into a movie—revealing how your strategy's market sensitivity morphs through cycles. Paired with your backend's automated yearly computation and interactive frontend chart, users get an immediate, intuitive feel for regime changes and hidden risks.
Ferson, W. E., & Schadt, R. W. (1996) – Measuring Fund Strategy and Performance in Changing Economic Conditions. Journal of Finance, 51(2), 425-461.
Blitz, D. (2013) – Benchmarking Low-Volatility Strategies. Journal of Portfolio Management, 40(2), 89-100.
Bodie, Z., Kane, A., & Marcus, A. – Investments (12 ed.), Ch. 24: Performance Attribution.
Brooks, R. D., Faff, R. W., & McKenzie, M. D. (1998). "Time-varying beta risk of Australian industry portfolios: A comparison of modelling techniques." Australian Journal of Management, 23(1), 1-22.
Mergner, S., & Bulla, J. (2008). "Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques." The European Journal of Finance, 14(8), 771-802.
Fama, E. F., & French, K. R. (1992). "The cross-section of expected stock returns." The Journal of Finance, 47(2), 427-465.
Alexander, C. (2008). Market Risk Analysis, Volume II: Practical Financial Econometrics. John Wiley & Sons.